Magnetic resonance is a known technique by which images of the interior of an examination object can be produced. In this case, the relationship between the precession frequencies (Larmor frequencies) of excited spins and the magnetic field strength of the magnetic field in the magnetic resonance scanner is used for position resolution. The magnetic field that is used is in this case composed of the basic magnetic field of the magnetic resonance scanner and applied gradient magnetic fields. Normal methods for reconstruction of image data records from magnetic resonance signals are predicated on a homogeneous basic magnetic field and strictly linear gradient magnetic fields.
The relationship between the Larmor frequencies and the magnetic field that is used results in geometric distortion along the frequency coding direction (read direction) in the image data records obtained from the magnetic resonance signals, if there are any inhomogeneities in the basic magnetic field. In this case, the distortion is proportional to local discrepancies in the basic magnetic field, and is inversely proportional to the strength of the frequency coding gradient.
If there are non-linearities in the gradient fields, the distortion occurs not only on the tomographic image plane, but also at right angles to this in the case of slice stimuli with a selection gradient. In practice, such inhomogeneities in the basic magnetic field and non-linearities in the gradient fields cannot be avoided completely. Nevertheless, the discrepancies in the basic magnetic field, that is to say the inhomogeneity, within a measurement volume of a magnetic resonance scanner should be less than 3 parts per million (ppm).
The resultant distortion in this case relates not only to the geometric position of the image data reconstructed from the magnetic resonance signals, but also to the reconstructed image signal strength. Attenuation of the image signal strength can occur in this case, for example, by dephasing of the spins in the presence of strong local basic field inhomogeneities. Further corrupting changes in the image signal strength are possible as a result of the spatial distribution of the intensity values, determined from the magnetic resonance signals, on an area whose size differs from the actual area.
The reasons why inhomogeneities occur in basic magnetic fields in magnetic resonance scanners are, for example, linked to the design, that is to say they are dependent, for example, on the design and winding geometry of the basic field magnet, the shielding and any shim apparatuses that are present. Inhomogeneities in the basic magnetic field caused in this way are static, that is to say they remain essentially constant over time.
Static inhomogeneities in the basic magnetic field may be measured, for example, with the aid of a measurement phantom at a number of measurement points on a surface of a conductor-free volume. The basic magnetic field can be determined at any point within the volume in a known manner from the values measured at the measurement points. In this case, the accuracy of the determination of the basic magnetic field depends on the one hand on the measurement accuracy of the measurement phantom, and on the other hand on the accuracy of the algorithm for determination of the basic magnetic field from the measurement points.
Further reasons for inhomogeneities in a magnetic field in a magnetic resonance scanner are, for example, susceptibility changes caused by an examination object being introduced into the magnetic resonance scanner, dynamic disturbances caused by eddy currents or artifacts such as “chemical shift”, flux artifacts or movements of the examination object. Inhomogeneities caused in this way depend on the respective situation, for example the nature of the examination and the examination object.
Any type of distortion in image data records is undesirable, in particular in medical image data records, since this corrupts a diagnosis, or at least makes it more difficult. Because of the various possible reasons for and types of distortion, various methods are already known in order to correct for the various types of distortion in image data records.
One method for distortion correction for gradient non-linearities in magnetic resonance scanners is known from DE 195 40 837 B4. In this case, two auxiliary data records which describe a shift of a measured point with respect to an actual point of a signal origin are used to carry out position corrections in the x and y directions. Intensity corrections are also used, in addition to the position corrections.
DE 198 29 850 C2 describes a method for reconstruction of a planar slice image from magnetic resonance signals in inhomogeneous magnetic fields. In this case, image elements of a planar slice image are produced from a plurality of original image elements on curved slices in the examination object.
WO 95/30908 A1 describes a method in which a generalized Fresnel transformation (GFT reconstruction) is carried out in the read direction. The GFT reconstruction takes account of any known position dependency of the main magnetic field in the read direction in order to allow distortion and intensity errors to be corrected for during the transformation from the measurement data space (k space) to the position space.
There is also a requirement for powerful methods for correction for distortion in image data records recorded by means of magnetic resonancing.